How to measure the angle between two functions

Extending the definition of angles and orthogonality beyond Euclidean spaces

This will surprise you: sine and cosine are orthogonal to each other.

Even the notion of the enclosed angle between sine and cosine is unclear, let alone its exact value. How do we even define the angle between two functions? This is not a trivial matter. What’s intuitive for vectors in the Euclidean plane is a mystery for objects such as functions.